I am studying a reliability paper "Analytical propagation of uncertainties through fault trees" (Hauptmanns 2002). Unfortunately, I cannot find an online copy to link to. The paper makes use of ye olde uniform pdf U(a,b) [http://en.wikipedia.org/wiki/ Uniform_distribution_(continuous)]. In the process, I'm also familiarizing myself with moments via wikipedia [http:// en.wikipedia.org/wiki/Moment_(mathematics)].
The papers states that the second moment of X~U(a,b) is:
E(X^2) = ( b^3 - a^3 ) / 3(b-a)
My own integration of x^2 from a to b yields (b^3-a^3)/3.
Can anyone point out where Hauptmanns's extra normalization factor 1/ (b-a) comes from? I thought he might have made a mistake and provided the normalized second moment, but then the normalization factor should be the variance, not 1/(b-a).